Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
198 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #121 |
| commutator, Frattini, cosocle | C42 | C23×C17 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C42×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C17×#493 | C2 | semidirect |
| 2. C17×#459 | C2 | semidirect |
| 3. C17×#436 | C2 | semidirect |
| 4. C17×#334 | C2 | semidirect |
| 5. C17×#331 | C2 | semidirect |
| 50. C8×C17 | D8 | semidirect |
| 51. #1687 | C17 | direct (N × H) |
| 64. #493 | C2×C17 | semidirect |
| 65. #459 | C2×C17 | semidirect |
| 66. #436 | C2×C17 | semidirect |
| 67. #334 | C2×C17 | semidirect |
| 68. #331 | C2×C17 | semidirect |
| 85. C17 | #1687 | direct (N × H) |
| 119. C8 | D8×C17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C17×#493 | 2 |
| C17×#459 | 2 |
| C17×#436 | 2 |
| C17×#334 | 2 |
| C17×#331 | 2 |
| #1687 | 17 |